What are the examples from nature we can use by storage of radioactive waste ? 

How can we say that it will be under the ground with little danger for the environment or people for more than 5000 years or 1 million years?   

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There are existing levels of low-level radiation that occur naturally in nature, such as coal, oil, and natural gas.  All these resources come from underground, so storage underground seems to be a pretty safe storage facility, since the surface and surrounding environment on top of these natural resources manage to do well.  There are different levels of radiation, ranging from high-level radiation, to medium-level, and finally, the aforementioned low-level radiation.  The more radiation a source gives off, the shorter the half-life, which is the amount of time it takes for half the source to decay into a stable form, that emits no radiation.  As is the case with radiation levels, the shorter the half-life, the faster the source loses its radiation danger.   Some sources have half-lives of thousands of years, so they must be maintained over a long period of time to prevent radiation poisioning of the environment.

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